Evidently Chris Cole has been
covering for me while I putz around. For those of you he's told about my dad,
here's the scoop:

A. He belongs to Kaiser, which
is scary all by itself, since they tend to be cost-conscious and complacent
even about a F***ING HUGE LUMP in his chest, growing rapidly.

B. After several months of
x-raying lump & saying we dunno what it is, somebody decides it's an aortic
aneurysm, which can blow at any time.

C. It's a misdiagnosis, but it
gets their asses moving, diagnostically. They find that it's a recurrence of
thyroid cancer from 1984. This is not necessarily horrible news, since it
tends to be curable.

D. However, months of jacking
around has allowed lump to engulf some of the clavicles & sternum.
Involved area must be excised in an eight-hour operation, which goes well,
taking only six hours.

E. However, six weeks later,
during the post-op iodine scan, it's found that the lump has regrown to it's
pre-op size.

F. The following week, we're
told the x-ray was misread. No lump at all. My dad is doing great. We're
optimistic about a complete recovery.

In the middle of this, my best
friend, a grad student in biochem who knew what he was doing, took cyanide.

Save your sympathy. If I had any
class, I wouldn't have mentioned this stuff at all and would have gotten Noesis
out on time. Thanks for letting me periodically try your patience.

Taking GRE's for credit is going
well. Taken four so far, plan on taking seven or eight more. Any of you could
accumulate years of college credit (one year per three-hour GRE!) doing the
same thing. Lemme know if you want to be bored with the specifics.

Just read that Ron Hoeflin is
also increasing his dues to $2.00 an issue. But here's my special deal to you,
since it's taken so long to get these issues out. Subscription money received
between January 5 and February 10 will be credited at a cost of $1.60 an
issue. After that, it's two bucks per. Please make checks payable to me,
rather than to Noesis. Thanks.

Daryl Inman recently had
his analogy tests printed in two high-circulation magazines. His Quest Test
appears in this month's Omni (It's the new "World's Hardest
I.Q. Test."), and his Crypto-Analogies Test appears in some
Canadian mag called SBT.

Robert Hannon and Norman
Hale--I've got material of yours to be stuck in the February issue.

SHORT FORM TEST
QUESTIONS AND ANSWERS TO DATE
WITH TWO NEW PROBLEMS

1.
Six squares can be joined edge-to-edge to form a two-dimensional shape. Some
of these shapes can be folded and joined along the squares' edges to form
complete cubes. How many different arrangements of six squares can be folded
into cubes? (Count reflections as distinct, but not rotations.) (Rick Rosner)

Answer:
20.

2.
Eight cubes can be joined face-to-face to form a three-dimensional shape. Some
of these shapes can be folded and joined (fourth-dimensionally) along the
cubes' faces to form hypercubes. How many different arrangements of eight
cubes can be folded to form hypercubes? (Again, reflections, but not
rotations, are distinct.) (Rick Rosner)

Hints:
I know the answer to the first problem, but the second is brutal. You don't
need to be able to think in 4D's to solve it, however. Each member of the set
of six-square shapes that can be folded into cubes may be transformed into any
other member through a series of 90-degree rotations of its constituent squares
around the squares' corners. 180-degree rotations are not allowed.

Similarly,
each member of the set of eight-cube shapes that can be folded into tesseracts
may be transformed into any other member through a series of 90-degree
rotations of its constituent cubes around the cubes' edges. Again, 180-degree
rotations aren't kosher. Any legal rotation produces a member of the set. All
you have to do is find one unfolded tesseract; the rest is just finding legal
rotations in three dimensions.

There
are as many ugly problems of this type as there are unfolded polyhedra and
hyperpolyhedra. The set of unfolded tetrahedra is trivial, and the set of
unfolded octahedra is easy, (Is it equivalent to the set of unfolded cubes? I
forget.) as is the set of unfolded hypertetrahedra. The sets of unfolded
icosohedra and dodecahedra are nasty (but equivalent?).

6.
You are lost in a half-planar forest, bounded on one side by a linear road.
The forest is too dense for you to be able to see the road until you walk right
up to it. You know that you are within one mile of the road, but are unable to
determine the direction to it. What is the length of the shortest path that
will guarantee your reaching the road? (Dean Inada)

Answer: miles

7.
If what does ?
(Chris Cole)

Answer:

8. (Rick Rosner)

Answer: a heptagon with concave
sides and minus its middle.

9. 0, 20, 6, 2, 5, 4, 2, 6, 0,
? (Jeffrey Wright)

Answer: one quadrillion
(smallest nonnegative integer containing each letter of the reverse alphabet)

10. Consider the
"volume" of an n-dimensional sphere of radius r. For n=1, 2, 3 the
"spheres" are the line segment, the circle, and the sphere, and the
volumes are 2r, pr2, and 4/3pr3. What is the volume of an
infinite-dimensional sphere, radius r? (Marshall Fox)

Answer: 0 ()

11. 95 : 98 :: VENITE : ?
(Pomfrit)

Answer: CANTATE

12. MINCES : EYES :: PORKIES :
? (Pomfrit)

Answer: LIES

13. 2823 : 5331 :: ELEPHANT : ?
(Pomfrit)

Answer: ANTIQUARIAN

14. (Sharp)

Answer: ?

15. At each point in the
Cartesian plane whose coordinates are both integers, an equilateral triangle is
centered. Each triangle is free to pivot around its center, all triangles are
the same size, and no triangles overlap. What is the maximum length of the
triangles' sides (and what is the maximum percentage of the plane's area they
can cover)? (Rosner)

Answer: ?

16. A goat is tied to a post on
the circumference of a circular meadow with a diameter of 100 meters.
Determine the goat's "radius of action" when the pasture ground
within its reach is exactly one half of the circle's area.

Answer: 57.9365 square meters

17. In what order are these
signs arranged?

E I S
H 5

Answer: Number of dots in Morse
code.

18. MORE : BOLSHEVIK :: LESS :
? (Eric Erlandson)

19. Given a solid sphere sliced
by n planes,

a. Find a general expression
for the maximum number of undivided volumes.

b. Calculate the number of
these volumes which are tetrahedrons, pentahedrons, etc., and the number of
volumes which have a section of the sphere surface as a "side." Do
the proportions of numbers of these various polyhedrons approach limits as n
goes to infinity? If so, calculate them. (Glenn Morrison, extracted from
letter later in this issue).

PROBLEM ANSWER

Dear Rick:

Here is my answer to problem 16,
page 12, in Noesis 74, about the goat. I get a radius of 57.936 meters.